How not to MISS an outlier: comparing three classic univariate methods and introducing a new one, the MAD–IQR–SD Simultaneous (MISS).

Outliers can strongly change statistical results, yet the three most widely used methods in psychology and neuroscience to detect them, Standard Deviation (SD), Interquartile Range (IQR), and Median Absolute Deviation (MAD), do not perform equally well across different data conditions. Importantly, these methods have rarely been compared systematically across a broad set of realistic scenarios, making it difficult for researchers to select an appropriate method in advance.In this study, we conducted large-scale simulations that varied distributional shape (normal, asymmetric, leptokurtic, uniform, asymmetric bimodal), sample size, outlier placement and outlier rate (0–40%). For each scenario, we assessed how SD, IQR, and MAD classified data points as valid or outlying by computing an accuracy score.Across the classic approaches, the most effective fixed thresholds were 2 SD, 2 IQR, and 3 MAD. SD performed well only when outliers were extremely rare (0-6%), but its accuracy dropped sharply as contamination increased. IQR was more robust at moderate outlier rates (8-20%), yet it became unreliable when many outliers were present or when distributions were asymmetric or bimodal. MAD showed the highest accuracy at high contamination levels (22-40%), although in leptokurtic (heavy-tailed) distributions both MAD and IQR were more biased than SD.To address these limitations, we introduce the MAD–IQR–SD Simultaneous (MISS) method, which integrates the three classical statistics using optimized weights identified through a genetic algorithm: 1.5 MAD [87.8%], 1 IQR [1.2%], 5 SD [11%]. Across all simulations, MISS achieved the highest overall accuracy (97.4%) and outperformed each classical method across most contexts.